I assume you don't need to deal with fiat? If so, then there is OKEX (10 BTC per 24 hours as a withdrawal limit) and KuCoin which has 1 BTC per day (decreased recently) but I wouldn't be surprised if they decided to enforce it all of a sudden just like Binance did.
But likely they can require for kyc at any point a time, like if suspecting someone's account? I believe this will be as they are still centralized. How also about FTX? I have not used both before, but I have seen some posts it is also suggested. The exchanges are centralized in this regard and have full control which can overide their customers control on their trading account, but in regards to OP's questions, this is still the best to go for. But we should know that centralized any exchange can go for kyc option at any point in time.